Finding Neff with only P-value, Odds Ratio, and individual frequencies in a meta-analysis

[Royce Clifford]

Hi!

I have a meta-analysis with four cohorts, have the total cases and controls for each cohort as well as MAF's for each cohort. 

For the meta-analysis I have an odds ratio and P value, but no Z and no standard error.

My formula for overall Z is qnorm(skula$P/2, lower.tail = FALSE).

My formula for standard error is log(OR)/z

When I try to calculate the cohort Neffs, I get negative numbers. What am I doing wrong? Here's a little sample of the data:

rsid................     ICE_freq     UK_freq    US_freq        Odds Ratio   P-value

rs113196488 ......         .1223              0.1061         0.1077                0.95075             .000100

Is it possible to derive Neff for each cohort from this data, or should I give this up and just derive it from the totals for all the cohorts?

Thanks!

Royce    

2

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[Elliot Tucker-Drob]

See the examples in https://github.com/GenomicSEM/GenomicSEM/wiki/2.1-Calculating-Sum-of-Effective-Sample-Size-and-Preparing-GWAS-Summary-Statistics

and the supplement to https://doi.org/10.1016/j.biopsych.2022.05.029 We show that you can estimate Neff from the logistic regression SE as 4/(2pq x logistic_SE^2).

Looks like you have the p value and Odds ratio. So in this case, I would 1) use qnorm to determine the Z statistic corresponding to the p value (taking care to obtain the p value for the two-sided test), 2) take the log of the odds ratio to get the logistic beta, and 3) solve for the SE given that Z=B/SE.

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[Royce Clifford]

Thanks for this. I calculated 

Z <- qnorm(P/2, lower.tail = TRUE)
beta <- log(OR)

SE <- beta/Z

Neff for each cohort <- 4/(2pq*SE^2)

Most of the values were reasonable - a few were infinite, some were not a number (NaN) and some were crazy, like 380 million. I guess that's why there's a cap.

Thanks for your help!

Royce

[Royce Clifford]

For my LDSC calculations, I'm getting crazy Total h2 liabilities for individual cohorts, crazy Total Observed Scale Genetic Covariance (g_cov), Total Observed Scale h2 of >>> 10000, and crazy Total liability scale genetic covariance between studies. I'm reasonably sure it is because of Neff, but I can't figure out what I'm doing wrong. Here are the stats for one of the studies:

cohorts          cases          controls            v             EffN

ICELAND        30802         278502           .10       110938

UKB                   9715         421332           .02         37984

US                      1888           24961           .07           7021

FINLAND           5667        169746           .03         21935

I had allele frequencies for each study, so I calculated Neff for ICELAND, for instance, as 4/((2 *  $ICE_freq * (1 -  ICE_freq)) *  se^2) and capped it recommended 1.1 and .5 EffNs, then summed the Neff's for the LDSC part. For standard error, I used the standard error of beta, which should be the log_se.

Correlations between the studies look very reasonable and Lambda GC and intercepts look great (maybe too good?). I just can't figure out what I'm doing wrong. Any input you might have would be very helpful.

Thanks!

Royce